Analyzing the full frequency distribution, we found that it is not well described by a Gaussian distribution but displays heavy tails. Therefore, more sophisticated distributions like Lévy-stable [1]} or q-Gaussian distributions [2]} should be considered when describing frequency distributions.
Choosing a small time interval around the trading actions every 15 minutes allowed us to reveal that trading has only little impact on the width (standard deviation) of the distribution but much larger impact on the heavy-tails. Nevertheless, even outside trading intervals, the frequency is not well-described by a Gaussian distribution.
A stochastic theory that neglects the effects of trading will therefore overestimate the heavy tails of the noise as those are significantly impacted by trading actions. However, such a theory will give a good approximation for the width of the distribution since the standard deviation does not depend as strongly on the trading actions.
We briefly reviewed some core results obtained in [3]} that allow to quantify the impact of power fluctuations on the power grid frequency even in non-Gaussian settings.
